What is the integral of 6ye^{5y^2} ?

The integral of 6ye^{5y^2} is 3/5 e^{5y^2}+C

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integral of 6ye^{5y^2}

\int 6 y e^{5 y^{2}} d y

\frac{3}{5} e^{5 y^{2}} + C

Solution steps

\int 6 y e^{5 y^{2}} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int y e^{5 y^{2}} d y

Apply u-substitution

: \int \frac{e ^{u}}{10} d u

= 6 \cdot \int \frac{e ^{u}}{10} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 6 \cdot \frac{1}{10} e^{u}

Substitute back

u = 5 y^{2}

= 6 \cdot \frac{1}{10} e^{5 y^{2}}

Simplify

6 \cdot \frac{1}{10} e^{5 y^{2}} : \frac{3}{5} e^{5 y^{2}}

= \frac{3}{5} e^{5 y^{2}}

Add a constant to the solution

= \frac{3}{5} e^{5 y^{2}} + C

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What is the integral of 6ye^{5y^2} ?
The integral of 6ye^{5y^2} is 3/5 e^{5y^2}+C